An A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problems

Sajid Memon, Neela Nataraj, Amiya Kumar Pani

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    11 Scopus citations

    Abstract

    In this article, a posteriori error estimates are derived for mixed finite element Galerkin approximations to second order linear parabolic initial and boundary value problems. Using mixed elliptic reconstructions, a posteriori error estimates in L∞(L2)- and L2(L2)-norms for the solution as well as its flux are proved for the semidiscrete scheme. Finally, based on a backward Euler method, a completely discrete scheme is analyzed and a posteriori error bounds are derived, which improves upon earlier results on a posteriori estimates of mixed finite element approximations to parabolic problems. Results of numerical experiments verifying the efficiency of the estimators have also been provided. © 2012 Society for Industrial and Applied Mathematics.
    Original languageEnglish (US)
    Pages (from-to)1367-1393
    Number of pages27
    JournalSIAM Journal on Numerical Analysis
    Volume50
    Issue number3
    DOIs
    StatePublished - Jan 2012

    Bibliographical note

    KAUST Repository Item: Exported on 2020-10-01
    Acknowledged KAUST grant number(s): KUK-C1-013-04
    Acknowledgements: Received by the editors January 15, 2010; accepted for publication (in revised form) January 3, 2012; published electronically May 31, 2012. This work was supported by the DST-CNPq Indo-Brazil Project DST/INT/Brazil/RPO-05/2007 (grant 490795/2007-2) and award KUK-C1-013-04 made by KAUST.
    This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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